Thank you for your question. "Credible," simply taken, means "believable." So a "credible profession of faith," as that phrase is often used, means a profession of faith that is believable, true in doctrine and not contradicted by the life, which is to be a life of faith and repentance.
This is what the Directory for the Public Worship of God says about the profession of faith: "Before permitting any one to make profession of his faith in the presence of the congregation, the session shall examine him in order to assure itself so far as possible that he possesses the doctrinal knowledge requisite for active faith in the Lord Jesus Christ, relies for salvation on the merits of Christ alone, and is determined by the grace of God to lead a Christian life" (DPW 4.A.3).
Those three elements (doctrinal knowledge, active faith, determination to lead a Christian life) must be present for a profession of faith to be valid or "credible." The local governing body of minister(s) and elders, the session, must be satisfied that these elements are present in any examined for profession of faith. That local governing body may gauge such in members differently, depending on their circumstances, but those elements must be present.
Ought we to be concerned about one who is developmentally challenged or disabled and not able to make a profession of faith, even a simple one? Not in the least. That youth or adult is a member of the church by virtue of their baptism and we entrust them to the Lord as much as we do our covenant children who have yet to make profession of faith. We need not fret over those dear ones among us who are unable to express their faith but look forward to the day when they, together with all the saints, will unendingly sing the praises of Him who is our Savior and our King.
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